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Comparison Properties of the CuntzSemigroup and Applications to C* -algebras

Published online by Cambridge University Press:  20 November 2018

Joan Bosa  and
Henning Petzka
Joan Bosa
Affiliation:
School of Mathematics and Statistics, niversity of Glasgow, 15 University Gardens, G12 8QW, Glasgow, UK e-mail: joan.bosa@glasgow.ac.uk
Henning Petzka
Affiliation:
Fraunhofer Institute for Intelligent Analysis and Information Systems IAIS, Schloss Birlinghoven, 53757 Sankt Augustin, Germany and, University of Bonn, Institut für Informatik III, Rheinische Friedrich-Wilhelms-Universität Bonn, Rཫmerstraße 164, 53117 Bonn, Germany e-mail: henning.petzka@iais.fraunhofer.de
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Abstract

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We study comparison properties in the category $\text{Cu}$ aiming to lift results to the ${{\text{C}}^{\text{*}}}$-algebraic setting. We introduce a new comparison property and relate it to both the corona factorization property $\left( \text{CFP} \right)$ and $\omega $-comparison. We show differences of all properties by providing examples that suggest that the corona factorization for ${{\text{C}}^{\text{*}}}$-algebras might allow for both finite and infinite projections. In addition, we show that Rørdam's simple, nuclear ${{\text{C}}^{\text{*}}}$-algebra with a finite and an inifnite projection does not have the $\text{CFP}$.

Keywords

46L3506F0546L0519K14classification of C*-algebrascuntz semigroup
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 1 , 01 February 2018 , pp. 26 - 52
Copyright
Copyright © Canadian Mathematical Society 2018

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